The authors wish to thank Steffi Höse, Claudia Klüppelberg, Ludger Overbeck, Ursula Walther, and two anonymous referees for comments and discussions.
CORRELATION UNDER STRESS IN NORMAL VARIANCE MIXTURE MODELS
Article first published online: 18 FEB 2013
© 2013 Wiley Periodicals, Inc.
How to Cite
Kalkbrener, M. and Packham, N. (2013), CORRELATION UNDER STRESS IN NORMAL VARIANCE MIXTURE MODELS. Mathematical Finance. doi: 10.1111/mafi.12029
The views expressed in this paper are those of the authors and do not necessarily reflect the position of Deutsche Bank AG.
- Article first published online: 18 FEB 2013
- Manuscript received October 2010; final revision received October 2012.
- stress testing;
- risk management;
- normal variance mixture distribution;
- multivariate normal distribution;
- multivariate t-distribution
We investigate correlations of asset returns in stress scenarios where a common risk factor is truncated. Our analysis is performed in the class of normal variance mixture (NVM) models, which encompasses many distributions commonly used in financial modeling. For the special cases of jointly normally and t-distributed asset returns we derive closed formulas for the correlation under stress. For the NVM distribution, we calculate the asymptotic limit of the correlation under stress, which depends on whether the variables are in the maximum domain of attraction of the Fréchet or Gumbel distribution. It turns out that correlations in heavy-tailed NVM models are less sensitive to stress than in medium- or light-tailed models. Our analysis sheds light on the suitability of this model class to serve as a quantitative framework for stress testing, and as such provides valuable information for risk and capital management in financial institutions, where NVM models are frequently used for assessing capital adequacy. We also demonstrate how our results can be applied for more prudent stress testing.